Woods, the hottest player on the PGA Tour with three victories this season and bidding this week for a second consecutive win, returned a roller-coaster 71 that included a double-bogey seven at the 17th.
"Most of the day I was slightly off and I definitely struggled with my green speeds," Woods told Golf Channel after totaling 31 putts in the opening round.
"My last three tournaments were awfully quick and I just didn't have the right speed out there."
IN PICTURES: Tiger Woods through the years
Woods, who overtook Jack Nicklaus in second place on the all-time list of PGA Tour winners with his two-shot triumph at the AT&T National on Sunday, is competing in the Greenbrier Classic for the first time. In the second round, Woods tees off at 1:20 pm Friday.
Asked if he was still adjusting to the Old White Course, Woods replied: "It takes a little bit of time, especially in our tournament conditions.
"The ball goes a little bit further because of adrenalin but I've got the feel of the golf course now. I'm going to hit some balls later and definitely putt for a while."
The smooth-swinging former world number one covered the back nine in a sizzling six-under 30 to shoot his lowest round on the U.S. circuit in four years.
"It's my first good round of the year that I would say I'm comfortable with," the 49-year-old Singh told reporters after mixing eight birdies with a lone bogey. "I've been playing well for a while now thinking one of these weeks it's going to click.
"It's so close. I get it going and then I have one bad round - either the third or the fourth round. But today was nice. I drove the ball well, hit a lot of good iron shots and made some putts."
Singh, a three-times major champion who has clinched 34 tournament wins on the PGA Tour, felt he had been putting himself under too much pressure in a bid to end his four-year title drought.
"I just have to believe," he said. "I've been trying too hard, forcing the issue a little bit.
"I've now stopped looking at the leaderboard. If you just have a number in mind and play around it, by the end of the week you'll be right there."
Singh tees off Friday at 1 pm.
Tour veteran Jeff Maggert opened with a six-birdie 64 to end the day level with fellow Americans Martin Flores and Jonathan Byrd.
Compatriots J.B. Holmes and U.S. Open champion Webb Simpson, Argentina's Andres Romero and South African Garth Mulroy were a further stroke back on 65.
Four-times major winner Phil Mickelson, like Woods, carded a 71, but was largely satisfied with his round after withdrawing from the Memorial tournament due to fatigue and tying for 65th at the U.S. Open in his previous two events.
"I hit a lot of good shots and so I was encouraged by that," the American left-hander said after mixing three birdies with two bogeys and a double-bogey at the par-four fifth.
"I haven't played well in the last six weeks so this was a good starting point, even though the score wasn't what I wanted."
Fellow American Scott Stallings, who claimed last year's title at The Greenbrier resort in a three-way playoff, opened with a 67. (Editing by Frank Pingue)